The Duggan–Schwartz theorem is a result in the field of social choice theory, specifically concerning the aggregation of preferences in social welfare functions. It addresses the impossibility of certain desirable properties in the context of collective decision-making. In its essence, the theorem states that under certain conditions, it is impossible to create a social welfare function that satisfies all of the following criteria: 1. **Unrestricted Domain:** Any individual preference order can be taken as input.
Topkis's theorem, named after Howard Topkis, is a result in the field of optimization and control theory, particularly concerning monotonic systems. The theorem provides conditions under which the optimal solutions of a dynamic programming problem are ordered in a certain way when the cost function is monotonic. Specifically, Topkis's theorem states that if the cost function is increasing in the state variable and the control variable, then the optimal value function will also be increasing.
Uzawa's theorem, also known in the context of economics, particularly pertains to optimal growth models and is named after the economist Hirofumi Uzawa. It provides conditions under which an economy can achieve a dynamic equilibrium while maximizing utility over time, often in the context of intertemporal choice and resource allocation. In its most common formulation, Uzawa's theorem is discussed in relation to the optimal growth problem in economics, specifically the Ramsey model.
The Gibbard–Satterthwaite theorem is a fundamental result in social choice theory and mechanism design that addresses the limitations of voting systems. It states that any voting rule (or voting mechanism) that satisfies certain reasonable conditions is susceptible to strategic manipulation, meaning that voters can gain by misrepresenting their true preferences.
Okishio's theorem is an economic theorem proposed by the Japanese economist Yoshio Okishio in the 1960s. The theorem addresses the relationship between technological change, the rate of profit, and the value of goods in a capitalist economy. It specifically concerns the effects of technical progress on the profitability of firms.
Ancient Egyptian mathematicians were individuals in ancient Egypt who contributed to the development and application of mathematics in various forms, particularly during the periods known as the Old Kingdom, Middle Kingdom, and New Kingdom, which spanned roughly from 2700 BCE to 1100 BCE. Mathematics in Ancient Egypt was primarily practical and focused on solving real-world problems related to agriculture, trade, construction, and astronomy.
Octavio Cordero Palacios was an Ecuadorian writer and politician, born on December 22, 1902, in the town of Loja and passing away on March 5, 1980. He is known for his contributions to Ecuadorian literature, particularly in the genres of poetry, short stories, and novels. His work often reflects the social and political issues of his time, intertwining themes of identity, culture, and the struggles of the Ecuadorian people.
Ptolemy can refer to several historical figures, concepts, or entities, depending on the context. Here are a few prominent references: 1. **Claudius Ptolemy**: A Greek-Roman mathematician, astronomer, geographer, and astrologer who lived in the 2nd century AD in Alexandria, Egypt.
Anelasticity is a property of materials that describes their time-dependent mechanical response under stress. In anelastic materials, the strain (deformation) does not completely recover when the applied stress is removed, meaning that there is a permanent deformation or change in structure after the removal of the stress. This behavior is different from that of elastic materials, which return to their original shape and dimensions once the stress is removed.
Creep is a time-dependent deformation of materials that occurs when they are subjected to a constant stress over an extended period. It is a crucial phenomenon in materials science and engineering, particularly for structures and components that experience prolonged loading conditions, such as bridges, buildings, pipelines, and high-temperature applications like turbines and reactors. Creep typically occurs in three stages: 1. **Primary Creep:** This initial stage involves a rapid rate of strain that gradually decreases over time.
GRADELA is a platform designed for the management and analysis of large-scale genomic data, particularly in the context of clinical and research applications. It facilitates the integration, analysis, and sharing of genomic data, enabling researchers and healthcare professionals to make informed decisions based on genetic insights. The platform focuses on improving the understanding of genetic variations and their implications for diseases, ultimately aiding in personalized medicine and targeted therapies.
The Gent hyperelastic model is a theoretical framework used to describe the large deformation behavior of rubber-like materials (elastomers). Developed by the researcher Brian Gent, the model specifically addresses the nonlinear elastic properties of these materials and is particularly useful for studying their behavior under various load conditions.
A Neo-Hookean solid is a type of hyperelastic (or Green elastic) material that is used to model the behavior of rubber-like materials under large deformations. It is characterized by a specific strain energy density function that is based on the idea of a Hookean solid, which is an ideal elastic material that follows Hooke's law. However, the Neo-Hookean model accounts for non-linear elastic behavior that occurs in materials when deformations are large.
The Perry–Robertson formula is a mathematical expression used in the field of risk assessment, specifically in the context of predicting the probability of certain events based on observed data. It is particularly prominent in the analysis of failure rates in engineering and reliability studies. The formula combines elements of Bayesian statistics and the Poisson distribution, allowing for the estimation of the rate of occurrence of rare events. This makes it particularly useful in fields like reliability engineering, where predicting failures or incidents is crucial.
Thermoelastic damping is a phenomenon that occurs in materials subjected to cyclic loading or deformation, where the internal energy dissipation is associated with thermal effects. It arises from the coupling of elastic and thermal responses of the material. When a material is deformed, it undergoes changes in temperature due to the irreversible processes of internal friction and the heat generated from the molecular motion and dislocations. This change in temperature can affect the material's elastic properties, creating a feedback loop.
As of my last knowledge update in October 2023, I don't have specific information on an individual named Alexandra M. Schmidt. It's possible that she could be a public figure, academic, or professional in a certain field, but more context would be needed to provide accurate information.
Ana María Aguilera can refer to different individuals or entities depending on the context. Without additional information, it's challenging to provide a precise answer. If you are referring to a specific person, such as a public figure, academic, artist, or any other notable individual, please provide more details. Additionally, it could also be the name of a place, business, or project. Clarifying the context will help in giving a more accurate response.
Angela Dean could refer to several different things or people, depending on the context. However, one of the most notable mentions is Angela Dean, the founder of the fashion brand "Deanzign," which is recognized for custom evening wear and bridal gowns. Angela Dean has also been known for her work in the fashion industry, particularly in the realm of celebrity dressing.
Eun Sug Park, also known as Eunsug Park, is not a widely recognized name in the context of historical, cultural, or contemporary figures. It may refer to a specific individual or a lesser-known entity that hasn't gained significant public attention.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact